This invention relates generally to calibration and compensation of accelerometers, and more specifically, to calibration and compensation of accelerometers with bias instability.
Most accelerometers incorporate one of two types of sensing elements. One sensing element type is a piezo-resistive sensor in which acceleration causes a resistance change in the sensing element itself. The resistance change thereby causes a change a time constant upon which accelerometer output is based. The other sensing element type is a capacitive sensor. In such a sensor, capacitance change is caused by a change in the spacing between capacitive elements due to acceleration. The capacitance change therefore causes a change in a time constant upon which accelerometer output is based.
Certain known accelerometers demonstrate bias instability. The bias instability is typically one or more of temperature cycle hysteresis and high gravitational force bias accumulation, which is sometimes referred to as anelastic bias response. These instabilities are of concern, and may prevent use of certain accelerometers, in particular applications, for example, guidance products. However, with proper calibration and compensation, the accelerometers can be used effectively in some applications, particularly in applications where bias accumulation occurs during testing but not in the actual application.
In one aspect, a method for determining compensation coefficients for accelerometers is provided. The method comprises estimating bias accumulation from measured accelerometer outputs, determining a corrected accelerometer output, and determining the compensation coefficients using the corrected accelerometer output.
In another aspect, a method for compensating for bias instabilities in accelerometers is provided. The method comprises removing temperature cycle hysteresis through temperature cycling, limiting durations of high acceleration load dwell times, and determining a corrected accelerometer output to compensate for bias accumulated during high acceleration load dwell times.
In still another aspect, a method of removing bias accumulation from an accelerometer measured output, the output being measured at a center point of time tc, of a high acceleration load interval of more than 1 g is provided. The method comprises estimating bias accumulation at the center point of time, tc, according to             1      2        ⁢          (                        a          ⁢                      xe2x80x83                    ⁢                      (                          t              2                        )                          -                  a          ⁢                      xe2x80x83                    ⁢                      (                          t              1                        )                              )        ,
where a(t1) is measured accelerometer output for a 1 g load at a time prior to a beginning of the high acceleration load interval, and a(t2) is measured accelerometer output for a 1 g load at a time after an end of the high acceleration load interval and correcting accelerometer output according to             a      c        =                  a        ⁢                  xe2x80x83                ⁢                  (                      t            c                    )                    -                        1          2                ⁢                  (                                    a              ⁢                              xe2x80x83                            ⁢                              (                                  t                  2                                )                                      -                          a              ⁢                              xe2x80x83                            ⁢                              (                                  t                  1                                )                                              )                      ,
where a(tc) is measured accelerometer output at the center point of the high acceleration load interval.
In yet another aspect, a system configured to determine compensation coefficients for an accelerometer is provided. The system comprises a computer comprising a processor and a memory, a rate table comprising a chamber, and a rate table controller connected to the computer and configured to run acceleration load profiles on the rate table, the acceleration load profiles stored in the memory of the computer. The system further comprises a temperature controller connected to the computer and configured to run temperature profiles in the chamber, the temperature profiles also stored in the memory of the computer. The system also comprises a device configured to measure output of accelerometers, the computer configured to receive and store output data from the device. The computer is also configured to estimate bias accumulation from measured accelerometer outputs, determine corrected accelerometer outputs, and determine compensation coefficients using the corrected accelerometer outputs.
In a further aspect, a computer for removing bias accumulation from accelerometer measured outputs is provided, the outputs being measured at a center point of time of a high acceleration load interval of more than 1 g. The computer is configured to estimate bias accumulation at the center point of time, tc, according to             1      2        ⁢          (                        a          ⁢                      xe2x80x83                    ⁢                      (                          t              2                        )                          -                  a          ⁢                      xe2x80x83                    ⁢                      (                          t              1                        )                              )        ,
where a(t1) is measured accelerometer output for a 1 g load at time prior to a beginning of the high acceleration load interval, and a(t2) is measured accelerometer output for a 1 g load at a time after an end of the high acceleration load interval and correct accelerometer output according to             a      c        =                  a        ⁢                  xe2x80x83                ⁢                  (                      t            c                    )                    -                        1          2                ⁢                  (                                    a              ⁢                              xe2x80x83                            ⁢                              (                                  t                  2                                )                                      -                          a              ⁢                              xe2x80x83                            ⁢                              (                                  t                  1                                )                                              )                      ,
where a(tc) is measured accelerometer output at the center point of time.